Internal problem ID [7462]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 743.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }-y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
dsolve(2*x*diff(y(x),x$2)-diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (2 \cos \left (2 \sqrt {x}\right ) \sqrt {x}-\sin \left (2 \sqrt {x}\right )\right )+c_{2} \left (2 \sin \left (2 \sqrt {x}\right ) \sqrt {x}+\cos \left (2 \sqrt {x}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 59
DSolve[2*x*y''[x]-y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{2 i \sqrt {x}} \left (2 \sqrt {x}+i\right )+\frac {1}{8} c_2 e^{-2 i \sqrt {x}} \left (1+2 i \sqrt {x}\right ) \\ \end{align*}